Abstract

Optimum stratification is the method of choosing the best boundaries that make strata internally homogeneous, given some sample allocation. In order to make the strata internally homogenous, the strata should be constructed in such a way that the strata variances for the characteristic under study be as small as possible. This could be achieved effectively by having the distribution of the main study variable known and create strata by cutting the range of the distribution at suitable points. If the frequency distribution of the study variable is unknown, it may be approximated from the past experience or some prior knowledge obtained at a recent study. In this paper the problem of finding Optimum Strata Boundaries (OSB) is considered as the problem of determining Optimum Strata Widths (OSW). The problem is formulated as a Mathematical Programming Problem (MPP), which minimizes the variance of the estimated population parameter under Neyman allocation subject to the restriction that sum of the widths of all the strata is equal to the total range of the distribution. The distributions of the study variable are considered as continuous with Triangular and Standard Normal density functions. The formulated MPPs, which turn out to be multistage decision problems, can then be solved using dynamic programming technique proposed by Bühler and Deutler (1975). Numerical examples are presented to illustrate the computational details. The results obtained are also compared with the method of Dalenius and Hodges (1959) with an example of normal distribution.